Demand for communication systems with greater capacity in recent years has focused much attention on methods such as orthogonal frequency division multiplexing (OFDM) and multiple-Input Multiple-Output (MIMO).
In OFDM, multiple signals are formed as a waveform by Inverse Discrete Fourier Transform process (IDFT) and output from the antenna. OFDM can be considered an orthogonal basi transformation (unitary transform) operation where multiple signals arrayed along the frequency axis are converted to multiple signals along a time axis.
When generating a complex signal string x—0−x_(N−1) in a time region by subjecting the complex signal string x—0−x_(N−1) of frequency region subcarrier 0 to N−1 to the IDFT process, where the frequency region signal vector X is expressed as Formula 1 and the time region signal vector T is expressed as Formula 2, then a Fourier transform string F can be used to express the conversion from T to X as shown in Formula 3.
                    X        =                  (                                                                      x                  0                                                                                    ⋮                                                                                      x                                      N                    -                    1                                                                                )                                    [                  Formula          ⁢                                          ⁢          1                ]                                T        =                  (                                                                      t                  0                                                                                    ⋮                                                                                      t                                      N                    -                    1                                                                                )                                    [                  Formula          ⁢                                          ⁢          2                ]            T=FHX  [Formula 3]
Here, F is an N×N matrix whose k-th row, l-th column component F_k,l is exp(−j2πkl/N)/sqrt(N) (Formula 4). The index of rows and columns in the matrix starts from 0. F is in other words made up of 0 to N−1 row, and 0 to N−1 column. The notation of vectors are also the same hereafter.
                              F                      k            ,            l                          =                              1                          N                                ⁢                      exp            ⁡                          (                                                -                  j                                ⁢                                                      2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    kl                                    N                                            )                                ⁢                                          ⁢                      (                                          0                ≤                k                <                N                            ,                              0                ≤                l                <                N                                      )                                              [                  Formula          ⁢                                          ⁢          4                ]            
Here, F is a matrix expressing the discrete Fourier transform (DFT). The H on the right shoulder of F expresses a conjugate transpose. The conjugate transpose of F is equivalent to an inverse matrix of F. The conjugate transpose of F is a matrix expressing the IDFT, and F is a unitary matrix.
Signal transmission efficiency can be boosted even in MIMO (Multiple-Input Multiple-Output) by unitary transform that treats the multiple signals as one vector and then mapping the signals in the multiple antennas. The conversion from the complex signal y—0 to y_(M−1) for multiplexing, to the output signal s—0 to s_(M−1) for multiple antennas M in the MIMO method is expressed in the following formulas 5, 6 and 7.
                    Y        =                  (                                                                      y                  0                                                                                    ⋮                                                                                      y                                      M                    -                    1                                                                                )                                    [                  Formula          ⁢                                          ⁢          5                ]                                S        =                  (                                                                      s                  0                                                                                    ⋮                                                                                      s                                      M                    -                    1                                                                                )                                    [                  Formula          ⁢                                          ⁢          6                ]            S=VY  [Formula 7]
Here, V is M×M unitary matrix.
A MIMO-OFDM method that utilizes both the OFDM and MIMO methods can be applied to achieve stable or high-speed communication. In this method in the transmitter, the unitary transform is first applied to MIMO antenna mapping, and then unitary transforms applied by IDFT for the OFDM method. Here, M is assumed as the degree of multiplexing in MIMO, and N is assumed as the number of subcarriers for OFDM. The original complex signal vectors Y are made up of M number of OFDM frequency region signals X(0) to X(M−1) as shown in Formulas 8 and 9. These OFDM frequency region signals are each made up of N number of signals.
                    Y        =                  (                                                                      X                  ⁡                                      (                    0                    )                                                                                                      ⋮                                                                                      X                  ⁡                                      (                                          M                      -                      1                                        )                                                                                )                                    [                  Formula          ⁢                                          ⁢          8                ]                                          X          ⁡                      (            m            )                          =                  (                                                                                          x                    0                                    ⁡                                      (                    m                    )                                                                                                      ⋮                                                                                                          x                                          N                      -                      1                                                        ⁡                                      (                    m                    )                                                                                )                                    [                  Formula          ⁢                                          ⁢          9                ]            
The output signal vector S from the antenna is made up of M number OFDM time region signals T(0) to T(M−1) as shown in Formulas 10 and 11. The OFDM time region signals are each made up of N number of signals.
                    S        =                  (                                                                      T                  ⁡                                      (                    0                    )                                                                                                      ⋮                                                                                      T                  ⁡                                      (                                          M                      -                      1                                        )                                                                                )                                    [                  Formula          ⁢                                          ⁢          10                ]                                          T          ⁡                      (            m            )                          =                  (                                                                                          t                    0                                    ⁡                                      (                    m                    )                                                                                                      ⋮                                                                                                          t                                          N                      -                      1                                                        ⁡                                      (                    m                    )                                                                                )                                    [                  Formula          ⁢                                          ⁢          11                ]            
If defined as shown above, then the conversion from Y to S can be expressed as shown in Formula 12 through Formula 14.
                              A          ⁢                      :                    ⁢                      A                          k              ,              l                                      =                  {                                                                      1                                                                      (                                          l                      =                                                                        N                          ×                                                      (                                                          k                              ⁢                                                                                                                          ⁢                              mod                              ⁢                                                                                                                          ⁢                              M                                                        )                                                                          +                                                  floor                          ⁢                                                                                                          ⁢                                                      (                                                          k                              ⁢                                                              /                                                            ⁢                              M                                                        )                                                                                                                )                                                                                                0                                                                      (                    others                    )                                                                        ⁢                                                  ⁢                          (                                                0                  ≤                  k                  <                  NM                                ,                                  0                  ≤                  1                  <                  NM                                            )                                                          [                  Formula          ⁢                                          ⁢          12                ]                                R        =                              (                                                                                F                    H                                                                                                                                                            0                                                                                                                                                                      ⋱                                                                                                                                                                      0                                                                                                                                                              F                    H                                                                        )                    ⁢                                    A              H                        ⁡                          (                                                                                          V                      ⁡                                              (                        0                        )                                                                                                                                                                                                    0                                                                                                                                                                                          ⋱                                                                                                                                                                                          0                                                                                                                                                                                V                      ⁡                                              (                                                  N                          -                          1                                                )                                                                                                        )                                ⁢          A                                    [                  Formula          ⁢                                          ⁢          13                ]            S=RY  [Formula 14]
Here, A is the NM×NM sequence conversion matrix between OFDM and MIMO. V(0) to V(N−1) are the unitary matrices for the MIMO antenna mapping in each subcarrier. R is also a unitary matrix and so the signal is also formed in the MIMO-OFDM method by unitary transformation and output from the antenna.
Each element prior to unitary transformation is hereafter called the communication mode. The OFDM subcarrier is also equivalent to communication mode.
In the unitary transform, a coefficient is applied to the communication mode signal and after summing an output signal is then generated. The communication mode signals are not correlated with each other and so the signals converted by summing are signals equivalent to Gaussian noise according to the central limit theorem. The signal amplitude distribution therefore expands widely. In other words, the signal has a large Peak-to-Average Power ratio (PAPR).
A larger PAPR causes problems when designing the transmitter. First of all, a digital-to-analog converter (DAC) with a large bit width is needed for handling the wide amplitude distribution, causing problems of cost and power consumption. Secondly, the problem of non-linear distortion in the power amplifier occurs during power amplification of the analog signal after DAC. These problems are described in the following drawings.
FIG. 2 is typical graph showing the amplifier gain (vertical axis is gain on left side, solid line) for the input signal power (horizontal axis: input power) to the power amplifier; and the power added efficiency (vertical axis is power added efficiency on right side, dashed line).
A large input power is preferable since the power added efficiency becomes higher as the input signal power increases. The gain is a fixed level when within the range of the specified input signal power but the gain decreases when the input power exceeds that range and non-linear characteristic appears. The signal waveform is distorted when this non-linear effect appears, and unwanted radiation is emitted outside the signal frequency band so this nonlinear effect must be avoided. Avoiding this non-linear effect requires restricting the input signal power to a region where the gain is linear. When amplifying a large PAPR signal, the average input signal power must be reduced so the peak is in a region where gain is linear; however, this lowers the power added efficiency.
To avoid these problems methods for reducing the PAPR have been studied. R. W. Baeuml, R. F. Fischer and J. B. Huber, “Reducing the Peak-to-Average Power Ratio of Multicarrier Modulation by Selected Mapping”, Electron. Lett., vol. 32, no. 22, pp. 2056-2057, October 1996, for example, discloses a selected mapping (SLM) method, and S. H. Mueller and J. B. Huber, “OFDM with Reduced Peak-to-Average Power Ratio by Optimum Combination of Partial Transmit Sequences”, Electron Lett., vol. 33, no. 5, pp. 368-369, February 1997, discloses a partial transmit sequence (PTS) method. Both methods apply mutually different phase rotations to the multiple communication mode signals to reduce the peak power value. These methods require that a phase rotation quantity supplied with the transmitter be conveyed as side information to the receiver in order to demodulate (restore) the communication mode signal within the receiver. A failure when supplying this side information causes demodulation (recovery) of all signals to fail.
J. Armstrong, “Peak-to-Average Power Reduction for OFDM by Repeated Clipping and Frequency Domain Filtering”, Electron. Lett., vol. 38, no. 5, pp. 246-247, February 2002 describes a clipping method. If the signal amplitude has exceeded a threshold value, then this method functions to limit the signal amplitude to the threshold value. Emissions might here radiate outside the signal frequency band so filters are utilized to eliminate components that are outside the frequency band. The filtering might generate new peaks but the technology in J. Armstrong, “Peak-to-Average Power Reduction for OFDM by Repeated Clipping and Frequency Domain Filtering”, Electron. Lett., vol. 38, no. 5, pp. 246-247, February 2002 applies clipping multiple times to suppress the occurrence of new peaks.
T. C. W. Schnek, P. F. M. Smulders and E. R. Fledderus, “Peak-to-Average Power Reduction in Space Division Multiplexing Based OFDM Systems through Spatial Shifting”, Electron. Lett., vol. 41, no. 15, pp. 860-861, July 2005 discloses a spatial shifting method which is a PAPR suppression method used with MIMO. This method substitutes the communication modes used for allotting the signals in order to lower the PAPR. To make optimum use of this method, side information must be conveyed to the receiver showing what communication mode to substitute. If there is a failure in supplying this side information then demodulation of all signals will fail.